1F. Ehtemam, 2H. Wang, 2A. van den Bogert & 1T. Kiemel

Copyright © 2017   1University of Maryland & 2Cleveland State University

Meeting of 2017-06-09

Using designed perturbation as input: Using measured perturbation as input: Slices of IRFs for designed perturbation as input: Slices of IRFs for measured perturbation as input: Impulse response (designed to measured) for both higher and lower accelerations: Step response (designed to measured) for both higher and lower accelerations: Tags: #designed #measured # emg #impulse #step

Meeting of 2017-06-23

The effect of input frequency bandwidth on impulse response function of the treadmill:
From top to bottom the bandwidth is changing from 5 Hz to 20 Hz (intervals of 5 Hz). Higher frequencies create less ringing. (more on ringing here: Ringing artifacts) The effect of input frequency bandwidth on step response function of the treadmill: The effect of input frequency bandwidth on IRF estimation for EMG (e.g. TA) : IRFs for thigh muscles: IRFs for hip extensors: Tags: #impulse #step #input #frequency #bandwidth #ringing #artifact

Meeting of 2017-07-07

Slices of IRFs (at phases of gait cycle for which the largest changes in the activity are observed) for TA and plantarflexors. IRFs were calculated using input bandwidths of 5, 8 and 10 Hz to see the effect of ringing artifacts on the responses.

Tags: #input #frequency #bandwidth #slices

Meeting of 2017-07-28

Tags: #emg #average #baseline #Winter

Meeting of 2017-08-11

Slices at the phase where the high and low perturbations each show maximum changes: Slices at the phase where the high perturbation shows maximum changes: Slices at the phase where the low perturbation shows maximum changes: Tags: #irf #emg #low #high

Meeting of 2017-08-25

Averaged EMG profiles

I subtracted the mean from each EMG signal before rectifying them. No filtering is done on the data. The data is averaged over all cycles, all trials and all subjects (15 subjects). Each cycle has 100 nodes in them. The heel-strike was identified using vertical coordinate of the heel marker. There were a few bad cycles (less than 5) for each trial that have been excluded. I will focus on EMG of RF here for two reasons: RF is a large muscle and identifying it is rather easy so with a little practice anyone should be able to place the sensor on the right spot to capture high quality signals which means that if signals are off for RF either sensors were not placed correctly for any of the muscles (which is unlikely) or something else is going on that has affected quality of all signals. The second reason is that RF was one of the muscles with a baseline that appeared to be high from the results I previously sent. Below is the RF plot. The baseline is close to 0.005 and the peak is around 0.011. The left shows the data without any normalization while the right shows the data that is normalized for each subject to RMS of their average (over trials) before data is averaged over all subjects. The top rows show the data for the high perturbation and the bottom shows the low perturbation data. The confidence intervals for the mean are shown for the non-normalized data (I skipped it for the normalized). Now comparing this with what Dana had from two subjects:

She had different perturbation conditions (left belt vs. right belt vs. both belts) and she presented the data for both perturbed and unperturbed legs. Over all conditions for RF the baseline changes between about 0.0025 to 0.005 (I don’t have the data so this is from visual inspection) and the peak changes between about 0.007 and 0.018. Comparing this to the numbers we have from the data Huawei and I collected I don’t think our data is bad. I think it is actually pretty good. I have looked at the data for individual subjects and I haven’t seen any subject showing any weird pattern. The confidence intervals also show that individual subjects don’t depart from the average by much. However, the story is different for normalized data. Normalizing using the aforementioned method results the baseline to go up. So to conclude this topic I think we need to answer these questions:
1. Do we think the data (as presented) is of acceptable quality meaning that there are no major artifacts or issues in the raw data? My answer to this question is yes but we can all discuss it to see what everyone is thinking.
2. If the answer to the first question is yes then how do we want to visualize the EMG data in a way that does not cause any distractions? Important points to think about here are these:

  • Do graphs have to start from zero? Most people think not including the origin (i.e. zero here) is misleading when presenting data (any data) so I think they should probably start from zero.
  • Do we have to have the same axis limit for all muscles? The same limits for all muscles results in some graphs to look weird since the peak to baseline ratio is different for different muscles. But the axis limits should definitely be the same for each muscle between different conditions.
  • Do we want to normalize the data before averaging between subjects or not? If the answer is yes then what method of averaging is the best and do we have to scale the axis after averaging in a way that minimizes distractions? Some people show their normalized data in a way that it always changes between zero and one. The answer here depends on which method we want to use for normalization if we want to do so.

EMG transient responses (i.e. slices of IRFs)

I showed some graphs in the last meeting and we discussed how we would like to present the data. The conclusion was that for both low and high perturbations we want to discuss the effect of perturbations over a few important phases. After going through different phases I picked a few phases for different muscle groups. The figure below shows the lower leg muscles responses. The horizontal axis shows a full gait cycle starting from toe-off. Notice that even though the zero on the axis is the heel-strike, the axis does not start from heel-strike. The reason for starting it from toe-off is that most interesting events happen around heel-strike (i.e. mid to late swing or early to mid stance). This means that keeping the heel-strike in the middle is a better way of presenting the changes. The green arrow in each figure shows the onset of perturbation. The red is high perturbation and blue is low (i.e. temperature analogy).

The plots for the lower leg show that all muscles respond to the perturbation delivered in early stance. TA shows an increase in the activity in response to the positive perturbation. As a reminder, with the current sign convention we have, positive perturbation is a step forward in the position of the belt which means that positive perturbation creates a plantarflexion. The calf muscles all show decreases in their activities in response to positive perturbation. Since the horizontal axis is one gait cycle and each cycle has 100 nodes and the data was presented with sampling rate of 100 Hz, this means that the latencies read from the graphs for the four muscles are between about 100 and 130 milliseconds. These responses are very straightforward to explain since they match our expectations from how TA and plantarflexors should respond to a perturbation applied to the foot when it is on the belt. However, we should keep in mind that TA has other responses that are not as easy as this one to explain. Looking at IRF plots below (left is for high perturbation and right is for low) we see that TA increases its activity in response to perturbation delivered at mid swing and decreases its activity in response to perturbation delivered in early swing. These responses have to be explained separately since they are unique to TA.

For upper leg muscles the late swing is suitable to explain the responses in quadriceps and hamstrings. All three quadriceps (figure below) decrease their activity in early stance in response to perturbation from late swing. This makes sense since the lower leg goes through a dorsiflexion in early stance so quadriceps from the upper leg become active to increase the knee angle and straighten the leg in preparation to raise the COM to the peak. But the positive perturbation now has introduced plantarflexion which can partly contribute to straightening of the leg so the activity of quadriceps becomes lower compared to what it should have been without this perturbation. We expect the opposite effect for hamstrings. This is clear in the activity of BF but ST doesn’t show any statistically significant change.

Apart form the responses discussed for the upper leg, hamstrings show a decrease in the activity in response to perturbation from early swing (figure below). The quadriceps don’t show much of a change in their activity during the same period which means that this should be discussed separately as a response unique to hamstrings.

So far I think the conclusion is that we have very clear responses in all leg muscles and the frequency domain approach we used was successful in identifying these responses. Also the latencies are reasonable even though this method cannot guarantee accurate estimation of latencies since the perturbation bandwidth is limited (i.e. there might be components of responses that we are missing because we have not perturbed the system over all frequencies it responds to) and also we do not include all harmonics involved in captured responses (i.e. in practice we assume after certain number of modes the harmonics are small enough that they could be ignored while in theory the number of harmonic modes that should be used to describe the response completely is infinite). One step that has to be followed for AP perturbations is to choose phases that best describe the responses of the hip and the trunk muscles. I have not done that yet.

Tags: #emg #slices #upperleg #thigh #lowerleg #shank #averages #baseline

Meeting of 2017-09-08

Statistics for EMGs

We use bootstapping to calculate p-values defined based on the maximum value of IRFs (the entire IRF not just one slice). This determines if the IRF that is averaged across all subjects is significantly different than zero or not. If the averaged IRF for a muscle is significantly different than zero then we can look at slices of the IRFs for that muscle otherwise responses for that muscle are not significant (p>0.05). The table below summarizes the results of tests for significance.
‘p’ means passed the test of significance and ‘f’ means failed.

Muscle Low perturbation High perturbation
TA p p
soleus p p
lGastroc p p
mGastroc p p
lGastroc p p
RF p p
vas lat p p
vas med p p
BF f p
ST f p
TFL f f
Gmed f f
Gmax f f
ESL f p
EST p p

Tags: #emg #statistics

Meeting of 2017-09-22

The effect of number of modes of harmonic transfer function on IRFs:

Mode zero (i.e. LTI approximation) Up to mode 3 Up to mode 6 Up to mode 9 Up to mode 12 Up to mode 15 Up to mode 18 Tags: #modes #irf

Meeting of 2017-10-06

Right lower leg Left lower leg Right upper leg (y labels are not correct) Left upper leg (y labels are not correct) Kinematics for right leg (early stance) Kinematics for right leg (late swing) Tags: #emg #kinematics #slices #ipsilateral #contralateral

Meeting of 2017-10-20

Lower leg ipsilateral (top) and contralateral (bottom) transient responses:
Upper leg ipsilateral (top) and contralateral (bottom) transient responses: IRFs for the heel and the belt:

Tags: #irf #slices #upperleg #lowerleg #ipsilateral #contralateral #belt #impulse #step

Meeting of 2017-11-03

Up to mode 9 Up to mode 12 Up to mode 15 Averages across all perturbation phases 15% of the cycle after onset of perturbation: individual subjects across all perturbation phases 15% of the cycle after onset of perturbation: Lower leg slices for two different phases of perturbation. The further we get from the heel strike the smaller TA responses become. So even though there is between subject variability in heel velocity close to heel strike, we can’t slice IRFs further away from heel strike if we want to show a meaningful response from TA. Tags: #modes #individual #heel #belt #kinematics #knee #leg #ankle #angle #hip

Meeting of 2017-11-17

Statistics for kinematics

‘p’ means passed the test of significance and ‘f’ means failed.
Right is ipsilateral and left is contralateral.

Kinematic variable Low perturbation High perturbation
Right Heel velocity p p
Right Leg angle p p
Right Ankle angle p p
Right Knee angle p p
Right Hip angle p p
———————— ———————— ————————
Left Heel velocity f p
Left Leg angle f p
Left Ankle angle f p
Left Knee angle f p
Left Hip angle p p
———————— ———————— ————————
AVG Heel velocity f p
AVG Leg angle p p
AVG Ankle angle p p
AVG Knee angle p p
AVG Hip angle p p

Kinematics for ipsilateral and contralateral legs for high perturbation slightly after heel strike.

Comments: The graph for contralateral leg has some errors.
Tags: #statistics #kinematics #leg #knee #ankle #hip #angle #ipsilateral #contralateral

Meeting of 2017-12-01

Early stance kinematic responses (joint angles and AP displacements)

6 month summary

Many questions have been asked during the analysis process in the last six months. I have addressed most of these questions through exploring the data in different ways which has resulted in significant progress towards the goal of the project. To restate the goal of the project, we started with the knowledge that walking is a limit cycle process and hypothesized that we could estimate responses of this system to mechanical perturbations of the treadmill assuming the system is linear and periodic (with respect to phase of gait). This would allow us to use harmonic transfer functions (HTF) method of analysis to establish the relationship between the input and the output in form of impulse response functions. So the goal was to show this method was viable to capture these responses accurately enough that the information provided would match the knowledge we had from the literature on how humans react to perturbations through spinal reflexes. Applying continuous perturbations of the treadmill is not a new concept. It has been done before (e.g. Moore et al. 2015). However, not many approaches have been developed that can reliably estimate responses to continuous treadmill perturbations. Our goal addresses this gap in the literature.
Here I list some major issues that have been addressed in the last six months and a summary of our discussions on them with the final conclusions:

  • The choice of the input signals (designed vs. measured perturbation). We showed that using designed perturbation compared to the measured perturbation (i.e. belt speed) results in better accuracy in estimating responses. The measured perturbation is obtained from a closed loop in which the walking of the subject on the belt affects the measured belt speed. In a later analysis (here), I showed that this effect is reflected in the speed of the belt averaged over all cycles. While we expect the average speed to be 1.3 m/s, we clearly see the small deviations (~ 1%) in belt speed as a result of the subject walking on the belt.

  • The choice of the input frequency bandwidth. We addressed the effect of input frequency bandwidth on estimated responses by looking at the impulse response and step response of the treadmill (i.e. between designed perturbation as treadmill input and measured perturbation as treadmill output). I don’t remember how we decided to use 5 Hz as the input bandwidth for designed perturbations but it turned out that the system had some responses above 5 Hz which resulted in ringing artifacts. The analysis showed that using a bandwidth of 8 Hz minimizes these artifacts (the unit here is not really hertz since these are normalized frequencies (i.e. normalized to the gait frequency) but since the gait frequency is close to 1 Hz you can think of them as hertz to make it easier to understand).

  • How to average EMG signals. We discussed the effect of method of normalizing EMG signals on averaged EMG (averaged over all cycles). We showed that the measured EMG data (before normalizing) is similar to other measurements. While the effect of normalizing is still an open question (i.e. what is the best way to normalize the signals for presentation) we decided to move on since this project in particular does not focus on the signals averaged over cycles.

  • All muscle responses and statistics. We showed that all lower leg and upper leg muscles have significant responses to the high amplitude perturbation. Hamstrings did not show significant responses to low perturbation and the hip muscles showed a mix of significant and non-significant responses to low and high perturbations. We concluded that further experiments are required to investigate the role of hip muscles in control of gait during perturbations but our results clearly present the contribution of the lower and upper leg muscles to control of walking.

  • The effect of number of harmonic modes on responses. We showed that the effect of number of harmonic modes used in estimation of responses is not a big effect and we decided that up to mode 9 provides a fair estimation of responses.

  • Left and right symmetry. We used the assumption that EMG activity was symmetric and looked at EMG responses for the left leg (i.e. contralateral leg) assuming they were half a cycle apart from the right leg. Results showed that for both lower leg and upper leg muscle groups the left leg responses were mostly insignificant. This could be due to the fact that the assumption of symmetry is not valid and does not capture the contribution of the contralateral leg or it could be that the perturbation only elicited responses in a small part of the cycle which could be damped by only activating the ipsilateral muscles.

  • Between subject variability in kinematics. We revisited the analysis of the impulse response and the step response of the treadmill this time comparing these responses to the impulse response (velocity) and the step response (position) of the heel marker. While the treadmill step response approached the value of one fairly quickly for all subjects, the heel step response to a perturbation delivered right after heel strike showed a large between subject variability. We then examined the effect of number of harmonic modes on this variability to see if using more modes would result in a lower variability. The effect of number of modes was insignificant. We then looked at diagonal slices of IRFs 15% after the onset of perturbation to see if the between subject variability is a function of the phase of the cycle. It turned out that the variability is small between 5% to 40% of the cycle. This is approximately the region where the foot is in complete contact with the belt. We then looked at EMG responses around for a perturbation delivered around 10% of the cycle (i.e. slightly away from heel-strike) to see if could have both significant EMG responses and low variability in heel kinematics but the response for TA at this point is not significant. We decided to present responses earlier where TA shows significant changes even though kinematic variability is larger.

  • Kinematic responses and statistics. We looked at statistical tests for various kinematic variables. The high perturbation always showed significant kinematic responses for both legs. The low perturbation had mixed results depending on the leg. This was not surprising since we saw earlier that low perturbation did not elicit significant responses in all muscles so we knew that the lower signal to noise ratio prevents us from seeing significant effects for some outputs.

  • Putting it all together. We had looked at EMG responses for both legs (assuming symmetry) earlier. Now we put the kinematic responses for both legs side by side to see if it provided us with some new information on reflexes. While the right leg (ipsilateral) showed increase in the leg angle, plantarflexion in the ankle angle and extension in the knee angle, all in agreement with a kinematic response to a decrease in belt speed that introduces plantarflexion, the left leg (contralateral) showed mixed results. The leg and hip angle responses after onset of perturbation were not significant for the left leg and the ankle angle response was a dorsiflexion instead of plantarflexion. We have to notice that the assumption of symmetry used here to plot responses of contralateral leg might not be a valid assumption so we should be very cautious in trying to make any conclusions by looking at assumed responses for the leg that was not measured. In addition to that, the responses for the contralateral leg during double support phase falls into the region for which we have a large between subject variability. This is from the time heel leaves the belt up into the swing phase. This as well affects any conclusions one might want to draw from these graphs. So in summary we have conclusive results for both EMG and kinematics from the leg we measured but the behavior of the other leg (contralateral) is up for debate and I think it needs further measurements.

  • What is next?. Regardless of when the perturbation is delivered, we can categorize EMG responses into two groups: one set of responses happen in mid-stance in response to the perturbation delivered in early stance. This is mainly the responses from plantarflexors. This corresponds to the single support phase which is not very difficult to understand. We have a good understanding of what is happening here.
    The second set of responses happen in early stance either in response to perturbation delivered in the late swing or the perturbation delivered in early stance. This corresponds to the double support phase which is more difficult to understand since it involves cooperation of both legs. Since we don’t have recordings from the contralateral leg, it is difficult to draw conclusions about the whole body movement. However, we still can explain the role of the ipsilateral leg during double support.
    What I will do next is to present both EMG and kinematic responses for the ipsilateral leg during single support. Then I will show the same responses during double support. This makes it easier to draw conclusions on what we have. After this I will show both left and right leg responses assuming total symmetry. We can discuss if anything conclusive comes out of this assumption.
    I think after this we should be in a good position to write the manuscript for these results.

Meeting of 2017-12-15

Early stance kinematic responses (joint angles)

Early stance kinematic responses (AP displacements)